Automatic calibration techniques and devices (also referred to as modules) are increasingly in demand for high frequency Vector Network Analyzers (VNAs) due to the reduction in operator errors, the reduced care and maintenance required of the calibration standards, and the potential for accuracy enhancement (due to issues with manual standards and procedures at higher frequencies). Most attempts at autocalibration modules rely on some switching of standards to be presented to the VNA. The measurements of these standards, coupled with previously known characterization data about these standards, allow a high quality calibration to be transferred to the VNA in question. At higher frequencies, the switches become lossier and more burdened with parasitics that make it difficult to render a set of standards that are sufficiently different for a good transfer calibration. Some approaches have used electromechanical switching structures with lower loss but these are not very repeatable and can lead to very slow and less accurate measurements. Some approaches use monolithic microwave integrated circuits (MMIC) structures to efficiently generate these standards but at a very high startup cost and with limited flexibility for future changes.
Most VNA automatic calibration schemes are based on the concept of a transfer calibration, e.g., as described in G. F. Engen, R. Judish, and J. Juroshek, “The multi-state two-port: an alternative transfer standard,” Proc. of 43rd ARFTG meeting, pp. 11-18, June 1994, which is incorporated by reference herein. The automatic calibration device represents some stable set of states, that when combined with some knowledge about these states (derived from a metrological grade calibration performed once), provides enough information to reproduce the metrology-grade calibration on another instrument (with some non-zero amount of degradation). The ‘knowledge’ mentioned above is merely measurements of all of the states of the automatic calibration device made using this good calibration. Typically the ‘good’ calibration is performed by the manufacturer of the automatic calibration device and is performed under tightly controlled, traceable conditions. Examples of automatic calibration devices that can be used to perform such ‘good’ calibrations are disclosed in the following patents, each of which is incorporated herein by reference: U.S. Pat. No. 5,548,538 to Grace et al., entitled “Internal Automatic Calibrator for Vector Network Analyzers”; U.S. Pat. No. 5,587,934, to Oldfield et al., entitled “Automatic VNA Calibration Apparatus”; and U.S. Pat. No. 5,552,714 to Adamian et al., entitled “Electronic Calibration Method and Apparatus”.
Because of cascading measurement uncertainties, the replicated calibrations will never be quite as good as the original. This leads to the question of what should the states of the automatic calibration device be to minimize this difference. To understand this, it is useful to look at a calibration algorithm. Traditionally, the transfer process is based on calibrating each reflectometer separately and then processing the transmission terms. As the critical part for this argument is the reflectometer portion, that path will be followed in the discussion below.
To perform single reflectometer calibrations, the minimum number of reflection standards is three, as can be appreciated from Equation 1 (Eq. 1.) below.
                              Γ          meas                =                  ed          +                                    et              ·                              Γ                act                                                    1              -                              eps                ·                                  Γ                  act                                                                                        (                  Eq          .                                          ⁢          1                )            where
the italicized terms represent unknown error terms describing the VNA to be calibrated (ed representing directivity, et representing reflection tracking, and eps representing source match),
Γact (or simply Γa) represents the reflection coefficient of the state as measured with the metro-grade calibration, and
Γmeas (or simply Γm) represents the same reflection coefficient as measured by the uncalibrated VNA-under-test.
For three standards, this problem can be linearized into a system of equations that are summarize in Equation 2 (Eq. 2) below.
                                          [                                                                                Γ                                          a                      ⁢                                                                                          ⁢                      1                                                                                        1                                                                                            -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          1                                                                                      ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        1                                                                                                                                                              Γ                                          a                      ⁢                                                                                          ⁢                      2                                                                                        1                                                                                            -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          2                                                                                      ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        2                                                                                                                                                              Γ                                          a                      ⁢                                                                                          ⁢                      3                                                                                        1                                                                                            -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          3                                                                                      ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        3                                                                                                                  ]                    ·                      [                                                            x                                                                              y                                                                              z                                                      ]                          =                  [                                                                      Γ                                      m                    ⁢                                                                                  ⁢                    1                                                                                                                        Γ                                      m                    ⁢                                                                                  ⁢                    2                                                                                                                        Γ                                      m                    ⁢                                                                                  ⁢                    3                                                                                ]                                    (                  Eq          .                                          ⁢          2                )            
where x, y, and z are combinations of the previous italicized unknowns.
In Equation 2, the coefficient matrix on the left is of more concern. Evaluating its determinant leads toΓa2Γa3Γm3−Γa2Γa3Γm2−Γa1Γa3Γm3+Γa1Γa3Γm1+Γa1Γa2Γm2−Γa1Γa2Γm1=Γm2Γa2(Γa1−Γa3)−Γm1Γa1(Γa2−Γa3)+Γm3Γa3(Γa2−Γa1)
If two standards have the same reflection coefficient (Γax=Γay, thus forcing Γmx=Γmy), the determinant vanishes thus leaving the problem insoluble. If two of the standards are even close (relative to measurement uncertainty), then the high sensitivity of the system will make the measurement practically useless (a small variation in trace noise leads to a wild variation in the calibration of the target VNA). This follows from the classical problem of solving a system of equations with a determinant near zero. This concept of sufficient separation of states is important and drives the design of transfer methods at higher frequencies.
In higher frequency switching structures, it is difficult to minimize losses and switch parasitics. PIN diodes, which are typically used in solid state versions of these structures, have losses that increase monotonically with frequency and a minimum capacitance (set by package and current technology) that perturb higher frequency performance. The bias circuitry for these diodes adds additional RF loss and mismatch. Also, since it takes very little physical size to create a large electrical length at frequencies above 40 GHz, the state reflection coefficients will move rapidly with frequency. These factors together lead to the problem that it is hard to keep three states sufficiently distinct at all frequencies (in a broadband system).
This leads to the concept of overdetermined calibrations where more than 3 states are provided and a M row version of Equation 2 is generated, as shown in Equation 3 (Eq. 3) below. Such a concept is described in part in an article entitled “An optimal multiline TRL calibration algorithm,” by D. F. Williams et al, IEEE MTT-S Digest, June 2003, pp. 1819-1822, which is incorporated herein by reference. As described in this article, this concept, can be solved using a simple least-squares approach (the best solution will be found in the sense that errors for the various constituent equations are minimized in a least squares sense) or through other techniques such as orthogonal distance regression. Orthogonal distance regression is described in an article entitled, “Over-determined calibration schemes for RF network analyzers employing generalised distance regression,” by M. Salter et al., Proc. of 62nd ARFTG meeting, December 2003, pp. 127-142, which is incorporated herein by reference. In either case, a solution for x, y and z is found that is ‘best’ in some sense and from this, the classical error terms for directivity (ed), source match (eps), and reflection tracking (et) can be easily found.
                                          [                                                                                Γ                                          a                      ⁢                                                                                          ⁢                      1                                                                                        1                                                                                            -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          1                                                                                      ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        1                                                                                                                                                              Γ                                          a                      ⁢                                                                                          ⁢                      2                                                                                        1                                                                                            -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          2                                                                                      ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        2                                                                                                                                          ⋮                                                  ⋮                                                  ⋮                                                                                                  Γ                    am                                                                    1                                                                                            -                                              Γ                        am                                                              ⁢                                          Γ                                              m                        ⁢                                                                                                  ⁢                        m                                                                                                                  ]                    ·                      [                                                            x                                                                              y                                                                              z                                                      ]                          =                  [                                                                      Γ                                      m                    ⁢                                                                                  ⁢                    1                                                                                                                        Γ                                      m                    ⁢                                                                                  ⁢                    2                                                                                                      ⋮                                                                                      Γ                                      m                    ⁢                                                                                  ⁢                    m                                                                                ]                                    (                  Eq          .                                          ⁢          3                )            
An additional modification than can be employed in this search for the ‘best’ solution is to weight the results based on some estimate of the uncertainty in the characterization values (or the measurements themselves), as described in an article entitled “Electronic and other industrial calibrations and error analysis,” by K. Wong, presented at IEEE MTT-S workshop WMK: Measurement Uncertainty for Network Analysis: State of the Art and New Directions, Philadelphia, Pa., June 2003, which is incorporated herein by reference. This can be done by simply scaling the equations by uncertainties U1, . . . , Um, as shown in Equation 4 (Eq. 4) below.
                                          [                                                                                                      Γ                                              a                        ⁢                                                                                                  ⁢                        1                                                              /                                          U                      1                                                                                                            1                    /                                          U                      1                                                                                                                                  -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          1                                                                                      ⁢                                                                  Γ                                                  m                          ⁢                                                                                                          ⁢                          1                                                                    /                                              U                        1                                                                                                                                                                                    Γ                                              a                        ⁢                                                                                                  ⁢                        2                                                              /                                          U                      2                                                                                                            1                    /                                          U                      2                                                                                                                                  -                                              Γ                                                  a                          ⁢                                                                                                          ⁢                          2                                                                                      ⁢                                                                  Γ                                                  m                          ⁢                                                                                                          ⁢                          2                                                                    /                                              U                        2                                                                                                                                          ⋮                                                  ⋮                                                  ⋮                                                                                                                        Γ                      am                                        /                                          U                      m                                                                                                            1                    /                                          U                      m                                                                                                                                  -                                              Γ                        am                                                              ⁢                                                                  Γ                                                  m                          ⁢                                                                                                          ⁢                          m                                                                    /                                              U                        m                                                                                                                  ]                    ·                      [                                                            x                                                                              y                                                                              z                                                      ]                          =                  [                                                                                          Γ                                          m                      ⁢                                                                                          ⁢                      1                                                        /                                      U                    1                                                                                                                                            Γ                                          m                      ⁢                                                                                          ⁢                      2                                                        /                                      U                    2                                                                                                      ⋮                                                                                                          Γ                                          m                      ⁢                                                                                          ⁢                      m                                                        /                                      U                    m                                                                                ]                                    (                  Eq          .                                          ⁢          4                )            
While a variety of lower frequency automatic calibration devices exist, these are not readily extensible to higher frequency work for the reasons mentioned above.
One high frequency apparatus and technique for calibrating a VNA is embodied in the Anristu model 36582KKF electromechanical autocalibration module, sold by Anritsu Company, Morgan Hill, Calif. While the three reflect states can be kept reasonably separate (very low loss in this switch type), it does suffer from repeatability issues inherent in electromechanical switches. Switch averaging schemes should be employed, but even with these, there is some accuracy degradation. Other potential issues are the slow speed and limited switch lifetime inherent in electromechanical designs.
A second alternative is to create the required switching and standards within an integrated circuit, as described in U.S. Pat. No. 6,914,436 to Liu et al., entitled “Electronic Calibration Circuit for Calibrating a Network Analyzer,” which is incorporated herein by reference. While this alternative significantly reduces the switch parasitics and electrical size of the structure, the engineering cost is very high, as are structural startup costs. Additionally, with this alternative reconfigurability is not possible without an entire new mask set and process run, which is very costly.
In both cases, multi-port versions have been envisioned (e.g., like the Anritsu 36584KF or similar). However, such multi-port versions typically just add an (N−1)-port switch in front of a 2-port automatic calibration structure. This can be appreciated from FIG. 1A, which shows an N-port VNA 101 (also known as a multi-port VNA) connected to a 2-port autocalibration module 100 using a single-pole N−1 throw switch 106. It is noted that the term multi-port, as used herein, refers to more than 2 ports. For example, a 2-port VNA is not a multi-port VNA, but a 4-port VNA is a multi-port VNA.
FIG. 1B illustrates exemplary details of a classical approach to an over-determined automatic calibration system having M standards, which can be used to implement the 2 port autocalibration module 100 of FIG. 1A. The system is referred to as an “over-determined” system because it uses more than the traditional three (open, load and short) calibration standards. For similar reasons to those mentioned above, here the M-throw switches 108 and 110 on each side can cause problems at high frequencies due to increasing losses and parasitics.
Accordingly, there is a desire to create a structure (operating from a few MHz or lower to beyond 50 GHz) with solid state switching and multiple standards, but still in a semi-discrete structure (separate switches from standards) to keep startup costs low and allow relatively quick reconfigurability.